Math Word Problem Helppp?! ?

Question

I don't understand these word problems.

1. Some students are to share the $540 expenses of a bus trip to Northwest Territories. When 5 students are unable to go, the cost per person is $1.50 more. How many students made the trip?

2. Normally, a factory produces 400 radios in "x" days. If the factory were to produce 20 more radios each day, then it would take 10 days less to produce 400 radios, caculate "x".

The area of a rectangle is 286 cm^2. If the longer side were decreased by 4 and the shorter side increased by 2 cm, the area would be reduced by 16 cm^2. Calculate the dimensions of the roginal rectangle.

4. A piece of wire 36 cm long is cut into two parts. Each part is bent into a square. The total area of the two squares is 45 cm^2. Find the sides of two squares.


I appreciate your help a lot! Thanks!

Answer 1

Hi Selena.

I have time today so this is my Xmas gift.



1.

x = # of students who made the trip

y = cost per student

: Total cost

xy = 540

(1) --> x = 540 / y

: Total cost "if"

(2) --> (x - 5)(y + 1.5) = 540

Equation (1) into (2)

(540/y - 5)(y + 1.5) = 540

In the first parenthesis the common denominator is y

((540 - 5y)/y)(y + 1.5) = 540

Multiplying both sides by y

(540 - 5y)(y + 1.5) = 540y

540y - 5y^2 + (1.5*540) - 7.5y = 540y

-5y^2 - 7.5y + 810 = 0

Get the roots by (-b +/- sqrt(b^2 - 4ac)) / 2a

y = -13.5 and 12

You cannot have a negative payment so the answer is 12$

Into (1)

x = 540 / y

x = 540 / 12

x = 45

So 45 persons did the trip coz I consider that the second part of the question is just an "if"

Check :

45 persons at 12$ = 540 :ok

(45 -5) persons * (12 + 1.5) = 540

40 * 13.5 = 540 :ok



2.

x = Original time to produce 400 radios (in days)

y = # radios produced per day

: Number of radios produced per days actually

400 / x = y

(1) --> y = 400 / x

: the "if" scenario

(2) --> y + 20 = 400 / (x-10)

Equation (1) into (2)

(400 / x) + 20 = 400 / (x - 10)

Common denominator on left side is x

(400 + 20x) / x = 400 / (x - 10)

400 + 20x = 400x / (x - 10)

(400 + 20x) (x - 10) = 400x

400x + 20x^2 - 4000 - 200x - 400x = 0

20x^2 - 200x - 4000 = 0

Get the roots by (-b +/- sqrt(b^2 - 4ac)) / 2a

x = 20 and -10

x cannot be negative so the answer is 20

Check :

It takes actually (400/x) = 400/20 = 20 days to make 400 radios

for 20 radios per day

If 20 more per day = 10 days less

At 40 radios per day it's gonna take 400/40 = 10 days to produce 400 radios

20 days actually - 10 days less = 10 days :ok



3.

x = shorter side

y = longer side

: Actual area

xy = 286

(1) --> x = 286 / y

: If scenario

(2) --> (x + 2)(y - 4) = 286 - 16

Equation (1) into (2)

(286/y + 2)(y - 4) = 270

Common denominator in the first parenthesis is y

((286 + 2y)/y)(y - 4) = 270

Multiplying both sides by y

(286 + 2y)(y - 4) = 270y

286y + 2y^2 - 1144 - 8y = 270y

2y^2 + 286y - 270y - 8y - 1144 = 0

2y^2 + 8y - 1144 = 0

Get the roots by (-b +/- sqrt(b^2 - 4ac)) / 2a

y = -26 and 22

Since a side cannot be negative, the answer is 22

and x = 286 / y = 286 / 22

x = 13

So x = 13 and y = 22

Check :

Actual area 13*22 = 286 :ok

If scenario 15*18 = 270 :ok



4.

x = side of first square

y = side of second square

: perimeters

4x + 4y = 36

Divide everything by 4

x + y = 9

(1) --> x = 9 - y

: Areas

(2) --> x^2 + y^2 = 45

Equation (1) into (2)

(9 - y)^2 + y^2 = 45

81 - 9y - 9y + y^2 + y^2 = 45

2y^2 - 18y + 81 = 45

2y^2 - 18y + 36 = 0

Get the roots by (-b +/- sqrt(b^2 - 4ac)) / 2a

y = 6 and 3

So the sides of the 2 squares are 6cm and 3cm

That means it doesn't matter if x or y equal 6 or 3

Check :

Perimeter = 4(3) + 4(6) = 12 + 24 = 36 :ok

Total area = 3*3 + 6*6 = 9 + 36 = 45 :ok

Answer 2

Problem 1 (x = no. of students):

540/x = (1,095 - 3x)/(2x - 10)

x(1,095 - 3x) = 540(2x - 10)

1,095x - 3x² = 1,080x - 5,400

3x² - 15x = 5,400

x² - 5x = 1,800

x² - 5/2x = 1,800 + (- 5/2)²

x² - 5/2x = 7,200/4 + 25/4

(x - 5/2)² = 7,225/4

x - 5/2 = 85/2

x = 90/2 or 45



Answer: 40 students (45 - 5) made the trip.



Proof:

= 40 students([$540/45 students] + $1.50 per student)

= 40 students($12 + $1.50 per student)

= 40 students($13.50 per student)

= $540.00



Too long. I've got no more time for other problems.

Answer 3

John has 5 bags of candy. 4 bags incorporate an entire of 80 4 products of candy Bag #5 includes the common of the 5 bags minus 4 Equation: (80 4+x)/5 <--- this might symbolize the common of the 5 bags Use the equation, and upload -4 via fact the value of bag 5 would be 4 below the common [(80 4+x)/5] - 4 = x <---flow the 4 over with the x (80 4+x)/5 = x+4 <---multiply the two sides by utilising 5 to cancel out the denominator (80 4+x) = 5(x+4) <---distribute the 5 to the numbers interior the parenthesis 80 4+x = 5x + 20 <---save the x's to a minimum of one component and non-'s to the different sixty 4 = 4x <---remedy for x x = sixteen Bag #5 had sixteen products of candy verify: (common of 5 bag) - 4 = entire Bag #5 [(Bag1+Bag2+Bag3+Bag4+Bag5)/5] - 4 = sixteen [(80 4+sixteen)/5] - 4 = sixteen (a hundred/5) - 4 = sixteen 20 - 4 = sixteen sixteen = sixteen actual

Answer 4

A lot of those are just systems of equations. Solve by elimination or substitution. The hardest part is converting it to numbers. Just think.

Answer 5

1. 45

2. 20

3. cant figure out sorry

4. 5cmX4cm

Answer 6

Hey...

FOCUS ....and Do ur homework !!!!